Recent and past research interests

• moving boundary problems (mean curvature flow, Hele-Shaw problem, Stefan problem etc.)
  
• numerical analysis for PDE (FDM, FEM, BEM etc.)
• singular perturbation for elliptic eigenvalue problems with large drift
  
• crack problems in fracture mechanics
• shape derivative and its application
• bulk-surface system  
  
• inverse Cauchy transform of domains
• pattern formation in reaction diffusion systems
  
• mathematical analysis of particle methods

Education
 
March 1990 : finishing study of Mathematics at Faculty of Science, Kyoto University
 
March 1992 : finishing master course study of Mathematics at Research Institute for Mathematical Sciences, Kyoto University
 
March 1996 : getting a Doctor degree of Science at Kyoto University
 
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Employment
 
April 1993 - March 1994 : JSPS research fellowship young scientist
 
April 1994 - September 1996 : Research Associate at Osaka Kyoiku University
 
October 1996 - October 2001 : Lecturer at Faculty of Science, Hiroshima University
 
November 2001 - present : Associate Professor at Faculty of Mathematics, Kyushu University
 
April 2007 - March 2008 : Visiting researcher at  Nečas Center for Mathematical Modeling (Czech Technical Univ. in Prague)
 

List of publications
 
M. Kimura,
Boundary Element Methods for Crack Problems,
Boundary Element Methods (Eds. S. Kobayashi, N. Nishimura),
Proceedings of the IABEM Symposium (Kyoto, October, 1991),
Springer-Verlag,(1992), pp.176-183.
 
M. Kimura,
Accurate Numerical Scheme for the Flow by Curvature,
Applied Mathematics Letters, Vol.7 (1994), pp.69-73.
 
M. Kimura,
Asymptotic estimation for the condition numbers in BEM, 
Numerische Mathematik, Vol.73 (1996), pp.209-233. 
 
M. Kimura,
Numerical analysis of moving boundary problems using 
the boundary tracking method,  
Japan J. Indust. Appl. Math., Vol.14 (1997), pp.373-398. 
 
M. Kimura, 
Time local existence of a moving boundary of the Hele-Shaw 
flow with suction,  
Euro. J. Appl. Math., Vol.10 (2000), pp.581-605. 
 
M. Kimura,
Shape derivative and linearization of moving boundary problems, 
GAKUTO International Series, Mathematical Sciences and 
Applications Vol.13 (2000), pp.167-179. 
 
M. Kimura and H. Notsu,
A level set method using the signed distance function. 
Japan J. Indust. Appl. Math. 19 (2002), No.3, pp.415-446. 
 
M. Kimura,
Numerical analysis of moving boundary problems, 
Sugaku Expositions, 15 (2002), No.1, pp.71-88.  
 
K. Shirakawa and M. Kimura,
Stability analysis for Allen-Cahn type equation   
associated with the total variation energy,   
Nonlinear Analysis, Vol.60, No.2 (2005), pp.257-282.
 
M. Kimura and S. Nagata, 
Precise asymptotic behaviour of the first eigenvalue of 
Sturm-Liouville problems with large drift, 
Trans. Japan Soc. Indust. Appl. Math. Vol.15, No.3 
(2005) pp.209-220. (in Japanese)
 
M. Kimura and I. Wakano, 
New mathematical approach to the energy release rate 
in crack extension, 
Trans. Japan Soc. Indust. Appl. Math. Vol.16, No.3 
(2006) pp.345-358. (in Japanese)
 
M.Kimura, H.Komura, M.Mimura, H.Miyoshi, T.Takaishi, and D.Ueyama,   
Adaptive mesh finite element method for pattern dynamics   
in reaction-diffusion systems.   
Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2005,   
COE Lecture Note Vol.3, Faculty of Mathematics, Kyushu University    
ISSN 1881-4042 (2006) pp.56-68.  
  
T.Nishida, K.Sugihara and M.Kimura,  
Stable marker-particle method for the Voronoi diagram in a flow field,  
J. Comp. Appl. Math. Vol.202 (2007) pp.377-391.
 
M.Kimura, H.Komura, M.Mimura, H.Miyoshi, T.Takaishi, and D.Ueyama, 
Quantitative study of adaptive mesh FEM with 
localization index of pattern  
Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2006,   
COE Lecture Note Vol.6, Faculty of Mathematics, Kyushu University    
ISSN 1881-4042 (2007) pp.114-136. 
 
M. Bene\v{s}, R. Chabiniok, M. Kimura, and K. Mikula,
Nonlinear Gauss-Seidel scheme for Allen-Cahn type systems, 
MAGIA 2007 Proceedings, Slovak University of Technology
in Bratislava, ISBN 978-80-227-2796-9, (2007) pp.29-35.
 
M. Bene\v{s}, M. Kimura, and S. Yazaki,
Analytical and numerical aspects on motion of polygonal curves
with constant area speed,
MAGIA 2007 Proceedings, Slovak University of Technology
in Bratislava, ISBN 978-80-227-2796-9, (2007) pp.127-141.
 
M.Kimura,
Shape derivative of minimum potential 
energy: abstract theory and applications,
to appear in 
Jind\v{r}ich Ne\v{c}as Center for Mathematical Modeling 
Lecture notes Volume IV, Topics in Mathematical Modeling 
(2008), pp.1-38.
 
M.Kimura,
Geometry of hypersurfaces and moving hypersurfaces 
in R^m ---for the study of moving boundary problems---,
to appear in 
Jind\v{r}ich Ne\v{c}as Center for Mathematical Modeling 
Lecture notes Volume IV, Topics in Mathematical Modeling 
(2008), pp.39-93.
 
M. Bene\v{s}, M. Kimura, P. Pau\v{s}, D. \v{S}ev\v{c}ovi\v{c}, 
T. Tsujikawa, and S. Yazaki,
Application of a curvature adjusted method in image segmentation,
Bulletin of the Institute of Mathematics, Academia Sinica, 
New Series, vol.3, no. 4 (2008), pp.509-523.
 
T. Takaishi and M. Kimura,  
 K. Ishijima and M. Kimura,  Vol. 59 (2011)  pp.85-90. 

Talks in international conferences
 
Boundary Element Methods for Crack Problems,
Symposium of the International Association for Boundary
Element Methods: IBEM-91 (Kyoto, Japan), Octorber 1991.
  
Uniform Convergence of Numerical Solutions for an Integral 
Equation of the First Kind appearing in BEM,
Japan-Russia joint seminar, Integral Equations in the Problems 
of Mathematical Physics (Khabarovsk, Russia) June-July 1992.
 
On the Inverse Cauchy Transform Using the Variational Inequality,
Numerical Analysis for Elasticity and Related Topics
(Kyoto, Japan) July 1994.
 
On an Explicit Formula of the Inverse Cauchy Transform,
Japan-Russia Joint Workshop, Inverse Problems and Il-posed Problems
(Tokyo, Japan) September 1994.
 
Inverse Cauchy Transform of Domains,
"The Carleman Estimate and Inverse Problems"
(Kyoto, Japan) May 1995.
 
Time Local Existence of the Moving Boundary of the Hele-Shaw Flow
with Suction, 
ESP-FBP Workshop ``Phase Transitions and Surface Tension"
(Weierstrass Institute for Applied Analysis and Stochastics, Berlin),
September 1996.
 
Convergence of a Boundary Tracking Method for the Curve Shortening Problem,
"Computation of Free Boundaries and Optimal Shapes" (Lamoura, France),
September 1996.
 
A level set method and its applicability and reliability, 
The fifth China-Japan Joint Seminar on Numerical Mathematics 
(Shanghai, China), August 2000.
 
A level set method and its applicability and reliability, 
Interphase VIII. Workshop on Numerical Methods for Free 
Boundary Problems (Berlin, Germany), Octorber 2000.  
 
A level set method for moving boundary problems, 
International Conference on Recent Advances in Computational 
Mathematics (ICRACM 2001), (Matsuyama, Japan) ，Octorber 2001. 
 
Variational mathematical model to quasi-stationary phase 
transition with the Gibbs-Thomson effect,
Czech-Japanese Seminar in Applied Mathematics
(Prague, Czech Republic), August 2004.
 
On a geometric variational problem related to the
quasi-stationary Stefan-Gibbs-Thomson problem,
Workshop on Mathematical and Numerical Analysis of
Nonlinear Phenomena (Tokyo Metropolitan University),
February 2005.
 
Adaptive mesh FEM for pattern formation in reaction 
diffusion systems,
2005 International Conference on Scientific Computation and 
Differential Equations (SciCADE05),（Nagoya, Japan), May 2005.
 
Adaptive mesh finite element method for pattern formation,
The Second Czech-Japanese Seminar in Applied Mathematics,
(Kuju, Japan), September 2005.
  
Adaptive mesh finite element method for several pattern formations,
2005 Taiwan-Japan Joint Workshop on Numerical Analysis and 
Scientific Computation, (Taipei, Taiwan), November 2005.
 
A quantitative study on adaptive FEM for several pattern formations,
Workshop on Numerical Analysis of Flow Problems 
and Validated Computations, (Nagasaki, Japan), November 2005.
 
Mathematical study on the energy release rate in fracture mechanics,
First Slovak-Japan workshop on computational mathematics,
(Bratislava, Slovakia), September 2006.
 
Exponential decay of the first eigenvalue of an elliptic problem 
with large drift,
Czech-Japanese seminar in applied mathematics 2006 
(Prague, Czech Republic), September 2006.
 
Mathematical formulation of the energy derivatives in crack evolution,
Inernational Symposium " Understanding of Complex Pattern Dynamics "
(Kobe, Japan), September 2006.
  
Energy release rate in crack evolution of brittle fracture,
Matematika na vysokychskolach (Herbertov, Czech Republic) September 2007.
 
Convergence of nonlinear Gauss-Seidel scheme for Allen-Cahn type systems,
Slovak-Austrian Mathematical Congress (Podbanske, Slovakia) September 2007.
 
Crystalline motion in Hele-Shaw cell,
DMHF2007 : COE Conference on the Development of Dynamic Mathematics 
with High Functionality 
(Kyushu University, Japan) October 2007.
 
Finite difference methods for Allen-Cahn/Cahn-Hilliard equations,
The Second China-Japan-Korea Conference on Numerical Mathematics
(Weihai, China) August 2008.

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